TY - JOUR
T1 - A port-Dirac formulation for thermodynamics of non-simple systems
AU - Yoshimura, Hiroaki
AU - Gay-Balmaz, François
N1 - Funding Information:
H.Y. is in part supported by JST CREST Grant Number JPMJCR1914, the MEXT Top Global University Project, Waseda University (SR 2021C-134), JSPS Grant-in-Aid for Scientific Research (17H01097) and the Organization for University Research Initiatives.
Publisher Copyright:
© The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
PY - 2021
Y1 - 2021
N2 - The paper presents a port-Dirac formulation for thermodynamics of non-simple systems, in which we consider a non-simple system whose thermodynamic states may be represented by several entropy variables. Here we regard such a non-simple system as an interconnected system with ports that can be represented by a port-Dirac system in the context of Dirac structures. We first show some extension of the Lagrange-d'Alembert principle for obtaining the evolution equations of such non-simple systems. Then, a Dirac structure is constructed on the Pontryagin bundle over a thermodynamic configuration manifold. Further, a port-Dirac dynamical formulation for such non-simple systems is demonstrated, where the developed evolution equations are to be equivalent with the generalized Lagrange-d'Alembert equations. The validity of the proposed approach is finally illustrated by two examples of an adiabatic piston and a resistive circuit with entropy production.
AB - The paper presents a port-Dirac formulation for thermodynamics of non-simple systems, in which we consider a non-simple system whose thermodynamic states may be represented by several entropy variables. Here we regard such a non-simple system as an interconnected system with ports that can be represented by a port-Dirac system in the context of Dirac structures. We first show some extension of the Lagrange-d'Alembert principle for obtaining the evolution equations of such non-simple systems. Then, a Dirac structure is constructed on the Pontryagin bundle over a thermodynamic configuration manifold. Further, a port-Dirac dynamical formulation for such non-simple systems is demonstrated, where the developed evolution equations are to be equivalent with the generalized Lagrange-d'Alembert equations. The validity of the proposed approach is finally illustrated by two examples of an adiabatic piston and a resistive circuit with entropy production.
KW - Adiabatic piston
KW - Dirac structures
KW - Electric circuit
KW - Non-simple systems
KW - Nonequilibrium thermodynamics
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U2 - 10.1016/j.ifacol.2021.11.051
DO - 10.1016/j.ifacol.2021.11.051
M3 - Conference article
AN - SCOPUS:85120990245
SN - 2405-8963
VL - 54
SP - 32
EP - 37
JO - IFAC-PapersOnLine
JF - IFAC-PapersOnLine
IS - 19
T2 - 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021
Y2 - 11 October 2021 through 13 October 2021
ER -